You will see bigger difference if your server is under heavy load. Network latency is playing a role here as well.
PHP script itself will run at the same speed inside PHP engine, LiteSpeed's advantage is resource management, PHP startup, passing request/response, etc. The faster your scripts run, the bigger difference you will see.
Under heavy load, Apache's performance will degrade greatly, while litespeed will hold much better.
If you want, you can benchmark a "Hello World" php script from localhost with "ab".